Finite Group Databasebeta

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C₇×#5771 #13061487

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

496 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 42 points:

(1,2,3,4,5,6,7)(8,9,10)(11,14,16,24)(12,19,17,31)(13,22,21,39)(15,28,29,26)(18,33,30,41)(20,38,32,36)(23,40,27,25)(34,42,37,35);(11,13,16,21)(12,18,17,30)(14,25,24,40)(15,27,29,23)(19,35,31,42)(20,37,32,34)(22,28,39,26)(33,38,41,36);(12,17)(13,21)(14,24)(20,32)(23,27)(26,28)(33,41)(35,42);(9,10)(11,12)(13,18)(14,19)(15,20)(16,17)(21,30)(22,33)(23,34)(24,31)(25,35)(26,36)(27,37)(28,38)(29,32)(39,41)(40,42)

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 10776);